### Archive

Archive for the ‘Mathmatical Theory’ Category

## Layering a Hex grid on the World

Here I will consider different methods of laying a hexgrid on a sphere. There are several reasons that you may want to do this:

a) To play a game on an existing system such as Google Earth
b) Regulate movement within your own game
c) To use as a system to import real maps into your own games.

Our planet is not a true sphere but for our puposes we will assume it and all other planets we encounter are regular spheres.

Using an Icosahedron
An Icosahedron is a 20 sided regular polygon, each face being an equilateral triangle. This shape will be familiar to wargamers that like to use 20 sided die.
This is not a perfect solution as the hexagons will not fit unless a pentagon is used at each apex of the Icosahedron.
The real advantage of this system is that you may use any scale that you choose, ie each of the 12 triangular sides within the Icosahedron may include as many hexagons as you wish, noting that the apex of each triangle will be a pentagon and not a hexagon.  For more detail search for Icosahedron Snyder or Geodesic.

This is not a solution if you want to zoom out to see an entire planet, as you will then see a flat sided planet.

To Be Continued…

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